Find the double integral

So I'm confused on how to take the first integral because of the radical... please explain how you came to your answer. (S=integral, so S:0,1 means the integral from 0 to 1, just to explain my notation)

So I'm confused on how to take the first integral because of the radical... please explain how you came to your answer. (S=integral, so S:0,1 means the integral from 0 to 1, just to explain my notation)

So for the inside integral, I got the answer to be $\displaystyle (3/2)x$, does that sound right to you? It seems like a strange amount of canceling. And when plugging into the final integral, I got the final answer to be 3.